Word problems based on formulation of linear programming problems.

2.   A manufacturer produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine 1 and 3 hours of work on machine 2 to produce a package of nuts. It takes 3 hours on machine 1 and 1 hour on machine 2 to produce a package of bolts. He earns a profit of Rs. 2.50 per package on nuts and Rs. 1 per package on bolts. Form a LPP to maximize his profit, if he operates each machine for almost 12 hours.

script

solution

Let x packages of nuts and y packages of bolts be produced. The objective of the manufacturer to maximize the profit is Total Time required on machine 1 to produce x packages of nuts and y packages of bolts is equal to   Total Time required on the machine 2 to produce x packages of nuts and y packages of bolts is equal to  s According to restrictions, For machine 1 For machine 2   Maximize z is equal to   Subject to constraints     To solve this graphically, let us take The lines are drawn using suitable points on the graph. The lines intersect at P(3,3) Now shade the region of intersection of the lines. The feasible region is OAPB For the corner point O(0,0), z= For the corner point A(4,0) For the corner point P(3,3,) For the corner point B(0,4) Clearly z is maximum at x=3 , y=3 and the maximum value is 10.50

2.50x + 1y     1x + 3y     3x + 1y           X + 3y ≤ 12 3x + y ≤ 12 and x,y≥0   2.50x + y   X + 3y ≤ 12 3x + y ≤ 12 X ≥ 0, y ≥ 0 X + 3y =12 3x + y = 12, x=0, y=0           O(0,0),A(4,0),P(3,3,),B(0,4) 2.5(0) +1(0)=0 2.5(4)+1(0)=10 2.5(3)+1(3)=10.5 2.5(0)+1(4)=4

3.   A shopkeeper deals in 2 items → wall hangings and artificial plants. He had a space to store 80 pieces and Rs. 15000 to invest. A wall hangings cost him Rs. 300 and artificial plant Rs. 150. He can sell a wall hanging at a profit of Rs. 50 and artificial plant at a profit of Rs. 18. Assuming that he can sell all the items that he buys, formulate a LPP in order to maximize his profit.\

script

solution

Let x be the number of wall hangings and y be the number of artificial plants. Profit of dealer is equal to Objective function z is equal to Since dealer invest atmost Rs. 15000 Therefore Or Also a dealer has space to store atmost 80 pieces. Therefore,   Maximize z is equal to Subject to constraints       To solve this graphically, we need to draw the graph Let us the draw the lines 2x + y ≤100 X + y ≤ 80 X ≥ 0, y ≥ 0 On the graph by using suitable points. The points of intersection are Then shade the region of intersection of these two lines The feasible points are OABC Now to obtain the maximum value; For The corner point O(0,0), z= For the corner point A(50,0) For the corner point B(20,60) For the corner point C(0,100) Clearly we get the maximum value of 2500 at A.(50,0)

50x + 18y 50x + 18y     300x + 150y ≤ 15000 2x + y ≤ 100     X + y ≤ 80 X ≥ 0, y ≥ 0 Z = 50x + 18y 2x + y ≤100 X + y ≤ 80 X ≥ 0, y ≥ 0                   (20,60)     O(0,0),A(50,0),B(20,60),(C(0,100)       50(0)+18(0)=0   50(50)+18(0)=2500 50(20)+18(60)=2080 50(0)+18(100)=1800

Posted Date: 7/23/2012 4:15:31 AM | Location : United States

Ask an Expert

Related Discussions:- Word problems based on formulation of linear programming, Assignment Help, Ask Question on Word problems based on formulation of linear programming, Get Answer, Expert's Help, Word problems based on formulation of linear programming Discussions

Write discussion on Word problems based on formulation of linear programming
Your posts are moderated

Write your message here..

Related Questions

LPP Sum, A paper mill produces two grades of paper viz., X and Y. Because o... A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Meaning and definition, Meaning and Definition If a group  of N observ... Meaning and Definition If a group  of N observations is  arranged in ascending or descending  order of magnitude then the  middle  value is  called  median of  these  observat

Unit 8, undertake the proposed research investigation in accordance with th... undertake the proposed research investigation in accordance with the agreed specification and procedures

#title.definition of graphical method ., full detailor theory on graphical ... full detailor theory on graphical method

Simple method, Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 =... Maximize Z= 3x1 + 2X2 Subject to the constraints: X1+ X2 = 4 X1 - X2 = 2 X 1, X2 = 0

Lpp, A paper mill produces two grades of paper viz., X and Y. Because of ra... A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

Data collection-requirement gathering methods, Data Collection / Requiremen... Data Collection / Requirement Gathering Methods 1. Discuss about the data collection or requirements gathering methods that will be used to conduct the research. 2. Discus

Answering lp problems, ABC Company manufactures both interior and exterior ... ABC Company manufactures both interior and exterior paints from 2 raw materials M1 and M2. The following table gives basic data of problem.     Exterior

Manufacturing operation , You are a manager at a medium sized manufacturing... You are a manager at a medium sized manufacturing operation that sells a customized product directly to the consumers and the data pattern is linear but it can have the occasion ra

Identify and comment on cultural similarities, You are required to analyse ... You are required to analyse the case study, as indicated under these headings: 1. Identify FIVE persons, bodies, organisations or groups in the case study. 2. For EACH of the